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Abstract

The degenerate four-wave-mixing process in the vicinity of an autoionizing state is studied theoretically in the context of perturbation theory. The autoionizing state is represented either by an isolated Fano profile or by the appropriate expression of the multichannel quantum-defect theory for the corresponding Rydberg series of autoionizing states. Analytic expressions for the third-order susceptibility are given together with realistic numerical estimates based on atomic parameters extracted from accurate spectroscopic data. It is demonstrated that the observation of the effect is feasible in extensively studied atomic systems (e.g., alkaline earths) with existing coherent light sources. Constraints on the atomic parameters that will facilitate the experimental observation of the effect are identified and shown to be frequently met in real atomic systems.

References

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Table 1

MQDT Parameters18 Employed in the Calculation of the Absorption and PC Spectra of Xe, Shown in Fig. 4a

Label

μ

R′

λ

[5p1/25nd3/2]J=1

2.314

-0.500

0.860

[5p1/25ns1/2]J=1

4.029

-0.169

1.187

a The total absorption spectrum is written as |μfi(Ec)|2=|μsi|2+24.17×|μdi|2+8.06, where |μsi|2 and |μdi|2 are given by Eq. (19) using the parameters appropriate for each autoionizing ns and nd series. The common threshold, 5p1/25, for both series is 108371.4cm-1, and the Rydberg constant for Xe is 109736.85cm-1. The numerical integration for the calculation of the PC spectrum begins at the first ionization threshold, 5p3/25, at 97934.4cm-1.

Table 2

MQDT Parameters20 Inserted in Eq. (24) for the Calculation of the Absorption and PC Spectra of Ba, Shown in Fig. 5a

Label

Threshold

μj (mod 1)

λj

Channel

Coupling Parameters Rkj′

1

2

3

6s1/2εs

42034.93cm-1

0

0

1

0

-0.1509

-0.1848

5d3/2nd

46908.78cm-1

0.4794

0.5791

2

0

-0.2115

5d5/2nd

47709.76cm-1

0.4400

1

3

0

a The Rydberg constant for Ba is 109736.87cm-1, and the lower limit for the numerical integration is the Ba first ionization threshold 6s1/2 at 42034.93cm-1.

Tables (2)

Table 1

MQDT Parameters18 Employed in the Calculation of the Absorption and PC Spectra of Xe, Shown in Fig. 4a

Label

μ

R′

λ

[5p1/25nd3/2]J=1

2.314

-0.500

0.860

[5p1/25ns1/2]J=1

4.029

-0.169

1.187

a The total absorption spectrum is written as |μfi(Ec)|2=|μsi|2+24.17×|μdi|2+8.06, where |μsi|2 and |μdi|2 are given by Eq. (19) using the parameters appropriate for each autoionizing ns and nd series. The common threshold, 5p1/25, for both series is 108371.4cm-1, and the Rydberg constant for Xe is 109736.85cm-1. The numerical integration for the calculation of the PC spectrum begins at the first ionization threshold, 5p3/25, at 97934.4cm-1.

Table 2

MQDT Parameters20 Inserted in Eq. (24) for the Calculation of the Absorption and PC Spectra of Ba, Shown in Fig. 5a

Label

Threshold

μj (mod 1)

λj

Channel

Coupling Parameters Rkj′

1

2

3

6s1/2εs

42034.93cm-1

0

0

1

0

-0.1509

-0.1848

5d3/2nd

46908.78cm-1

0.4794

0.5791

2

0

-0.2115

5d5/2nd

47709.76cm-1

0.4400

1

3

0

a The Rydberg constant for Ba is 109736.87cm-1, and the lower limit for the numerical integration is the Ba first ionization threshold 6s1/2 at 42034.93cm-1.